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Week 7: Internal stresses and moments of infinitely long bars

by: Eleanor Notetaker

Week 7: Internal stresses and moments of infinitely long bars coe 3001 I

Marketplace > Georgia Institute of Technology > Engineering and Tech > coe 3001 I > Week 7 Internal stresses and moments of infinitely long bars
Eleanor Notetaker
Georgia Tech
Deformable Bodies
Dr. Kennedy

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We talk about how to find internal stresses and strains on bars that are "infinitely" long. We start with continuous stress, change to point stress, and finish with a point moment that is the forc...
Deformable Bodies
Dr. Kennedy
Class Notes
25 ?




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This 4 page Class Notes was uploaded by Eleanor Notetaker on Sunday October 4, 2015. The Class Notes belongs to coe 3001 I at Georgia Institute of Technology taught by Dr. Kennedy in Summer 2015. Since its upload, it has received 38 views. For similar materials see Deformable Bodies in Engineering and Tech at Georgia Institute of Technology.


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Date Created: 10/04/15
COE 3001 Mechanics of Deformable Bodies Week 7 Shear forcebendin moment relations Only distributed loads acting Z Forces in y Vx Vxll Ax qxAx0 dV dx Ax qx O dV 5 QM dV 0 and VX E constant If qx0 then 3 dV If qxq0 then Eq0 and VXq0c Z Moments at A Mx Mx l AAx VxAx Ax qxA 720 AxvxAxAx2qxA320 Vxll Ax qxo iigoil Aj th Ax qx 0 2 42Vx Point Loads COE 3001 Mechanics of Deformable Bodies Week 7 Vx VxAV PO AV P Moment at A Ax Ax MxAM Mx 7VxAV 7Vx O Ax AM72VxAV AMgt0 as Axgt0 so AM0 Point Moments Z Forces Vx VxAV0 A V 0 Z Moments at A MxAM MxMP VxAV Vx0 AMMP 2VxAVO lim AMMP A 2x2VxAVO Axgt0 AMz MP 5 Stresses in beams 0 Loads on beam produce internal shear bending and axial resultants COE 3001 Mechanics of Deformable Bodies Week 7 b Assume that crosssection is symmetric in Xy plane Pure bending 0 Only bending no shear Nonuniform bending 0 Bending moment non0 shear Pure bending Curvature 0 L ction Note only drawing centerline of beam 9 E radius of curvature l K p E curvature From the diagram ds pde 1 d9 K p ds Because the de ection is small ds z dx d r gtK dx Longitudinal Stresses in beams undc COE 3001 Mechanics of Deformable Bodies deformed Week 7 geometry before load is applied 0 Top portion under compression 0 Bottom portion under tension 0 Centerline No strainstresses 0 Neutral surface axis position in beam Where stressstrain are 0 dsp B dl39p yd9 gtdl39p cB ydezds yde zdx yde undeformed d1 dx 6 dlI dl dx yde dx 6 dl dx


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